Rank and border rank of Kronecker powers of tensors and Strassen's laser method

We prove that the border rank of the Kronecker square of the little Coppersmith–Winograd tensor $$T_{cw,q}$$ T c w , q is the square of its border rank for $$q > 2$$ q > 2 and that the border rank of its Kronecker cube is the cube of its border rank for $$q > 4$$ q > 4 . This answers questions raised implicitly by Coppersmith & Winograd (1990, §11) and explicitly by Bläser (2013, Problem 9.8) and rules out the possibility of proving new upper bounds on the exponent of matrix multiplication using the square or cube of a little Coppersmith–Winograd tensor in this range.In the positive direction, we enlarge the list of explicit tensors potentially useful for Strassen's laser method, introducing a skew-symmetric version of the Coppersmith–Winograd tensor, $$T_{skewcw,q}$$ T s k e w c w , q . For $$q = 2$$ q = 2 , the Kronecker square of this tensor coincides with the $$3\times 3$$ 3 × 3 determinant polynomial, $$\det_{3} \in \mathbb{C}^{9} \otimes \mathbb{C}^{9} \otimes \mathbb{C}^{9}$$ det 3 ∈ C 9 ⊗ C 9 ⊗ C 9 , regarded as a tensor. We show that this tensor could potentially be used to show that the exponent of matrix multiplication is two.We determine new upper bounds for the (Waring) rank and the (Waring) border rank of $$\det_3$$ det 3 , exhibiting a strict submultiplicative behaviour for $$T_{skewcw,2}$$ T s k e w c w , 2 which is promising for the laser method.We establish general results regarding border ranks of Kronecker powers of tensors, and make a detailed study of Kronecker squares of tensors in $$\mathbb{C}^{3} \otimes \mathbb{C}^{3} \otimes \mathbb{C}^{3}$$ C 3 ⊗ C 3 ⊗ C 3 .

Research of Phase Behavior in Natural Gas Drive Process and Its Application in T_D Reservoir with HTHP

Different from other gas drive processes, phase behavior performs more significant roles in natural gas drive process. The main reason is that more severe mass transfer effect and similar phase solubility effect have been caused by multicomponent interaction. This paper provides a series of methods to study the phase behavior in natural gas drive process, aiming to reveal further mechanism and give technical supports to the on-site practice in T_D Reservoir with HTHP. Four key parameters of natural gas drive have been determined. Firstly, laboratory compounding method has been improved to obtain real components of formation fluids and actual injected gas at formation condition (140°C, 45MPa). Secondly, 19 sets of slim tube test has been carried to determine MMP (minimum miscible pressure) and the injected gas components ensuring miscibility. Thirdly, swelling test and laser method have been used to separately obtain the viscosity reduction degree and solid deposition effects. Finally, multiple contact test has been carried to describe the miscibility behavior. All the above have been applied in T_D Reservoir. Conclusions could be drawn from the results obtained by the methods above. Firstly, swelling capacity of crude oil could be enhanced by natural gas for the formation volume factor of crude oil in T_D Reservoir increased by 57% and the viscosity decreased by 83% after natural gas injection. Secondly, MMP of dry gas and crude oil in T_D Reservoir is 43.5MPa with a miscible displacement efficiency above 90% (>30% compared with immiscible displacement efficiency), and the content of N2+C1 should be controlled over 88%. Thirdly, results of 5 levels contact experiments shows that miscibility behavior of natural gas and oil from T_D Reservoir performs an evaporative-condensate composite miscible process in which the condensate miscible process takes the lead. Finally, obvious solid point has not been observed in natural gas drive process of crude oil from T_D Reservoir at the formation temperature, and the effect of solid deposition on the fluid flow in formation could be ignored because of trace amount of solid solution (<1mg/ml) and minute formation permeability damage (<8%). The achievements above have been applied in T_D Reservoir as one of the important technical means supporting over 350,000 tons increased production by natural gas drive. A systematic methods have been reorganized to research the phase behavior in natural gas drive process and half of these methods mentioned above get partially improvement. These physical simulation experiments have covered most mainly processes and the key parameters in reservoirs with HTHP and natural gas drive, including mass transfer, viscosity, expansion, volume coefficient, MMP, miscibility behavior and solid deposition. Every experiment gives a quantitative analysis which possesses satisfied practicability in field application.

Analysis of the polydispersity of soil-like bodies in glacier environments by the laser light scattering (diffraction) method

This study presents the results of polydispersity analysis of soil-like bodies from two various polar regions using the laser light scattering method. The differences in the particle size distribution of cryoconite samples from the Anuchin Glacier (Antarctica) and the Mushketov Glacier (Arctic) are described. The samples obtained from the Mushketov Glacier are characterized by a finer particle size distribution than samples collected on the Anuchin Glacier. While comparing our results with previously published studies, it was found that the method of laser light scattering shows a lower content of small fractions (<0.05 mm) compared to the classical methods of sedimentation, since these methods are based on fundamentally different physical principles. The laser method used requires low amounts of samples (0.2–0.5 g), while the classical sedimentary method uses a higher gravimetric portion of cryoconite (5–10 g), which is critical for field sampling.

Le rôle de la matrice extracellulaire dans la régénération des nerfs moteurs

The motor neurons (MN) form the ultimate route to convey the commands from the central nervous system to muscles. During development, MN extend axons that follow stereotyped trajectories to their muscle targets, guided by various attractive and repulsive molecular cues. Extracellular matrix (ECM) is a major source of guidance cues, but its role in axonal development and regeneration remains poorly documented. Regenerating axons are able to return to their synaptic target following their original trajectory. The same guidance cues could be thus involved in motor nerve regeneration. Zebrafish has become a popular model system in understanding the development of the peripheral nervous system. Thanks to the generation of fluorescent transgenic lines and the optical transparency of embryos and larvae, it allows direct visualization of axonogenesis. Additionally, and contrary to humans, its remarkable capacity to regenerate makes it well suited for the study of nerve regeneration. A laser method to ablate nerves in living zebrafish larvae has been developed in our laboratory that, combined with the use of the fluorescent mnx1:gfp zebrafish transgenic line, allows the follow up of the dynamics of the nerve regeneration process. To study the role of ECM proteins present in the axonal path, mutant lines for different ECM proteins (already available in our laboratory or generated in mnx1:gfp fish using CRISPR-Cas9 method) will be used to analyze their role during the regeneration process. These mutant lines for ECM will be crossed with existing fluorescent transgenic lines to visualize different cell types involved in the nerve regeneration, such as macrophages (mfap4:mcherry), neutrophils (mpx:gfp) or even Schwann cells (sox10:mrfp). Overall, this study will depict the role of ECM in nerve regeneration and will provide essential knowledge for the development of new biomaterials to promote the regeneration of injured motor nerves.

Oscillation Modes of Weld Pool in Stationary GTA Welding Using Structure Laser Method

Researchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision method. However, the deficiency of simulation software will result in significant capital expenditure. Both simulations and experiments are performed in this study, and the Bessel equation is used to analyze the oscillation mode of a weld pool. The laser dot matrix images of (0, 1), (1, 1), (2, 1), and (0, 2) oscillation modes at different times are obtained via structured laser optical measurement simulation. The oscillation mode of a stationary gas tungsten arc weld pool is analyzed based on laser dot matrix images obtained from a structure laser experiment. Results show that the simulated laser dot matrix images are consistent with the experiment results. The oscillation mode of the weld pool can be recognized based on the laser dot matrix image. This study not only provides conditions for assessing the penetrating state of a weld pool, but also enable a further understanding of the oscillation mode of a weld pool and the development of more effective observation methods and measurement tools to effectively control and improve welding quality.

Molybdenum oxide based sensors

In this review article were considered the works of electrochemical sensors modified with molybdenum oxide. The work of sensors based on molybdenum oxide was systematized, a comparison table was developed, the sensors were classified according to the purpose of use. Methods of molybdenum oxide synthesis used to modify the working electrode in electrochemical sensors were considered. The various methods have been used to synthesize molybdenum oxide, such as a thermal, hydrothermal, electrochemical, electric spark, pulsed laser method, acid condensation, electrophoretic precipitation, pulse potential precipitation. The main parameters of the molybdenum oxide modified sensors, such as the detection limit, linear range, response time, sensitivity, and other parameters were compared. As a result of studies, it was found that molybdenum oxide is selected as a modifying material in electrochemical sensors due to the unique physicochemical properties of molybdenum oxide, in particular because of mechanical strength, electrical conductivity, electro catalytic activity, crystallinity. The features of electrochemical biosensors coated with molybdenum oxide were described for the detection of important compounds in specific samples. Sensors based on molybdenum oxide have been used for detection of glucose, dopamine, ethanol, ascorbic acid, troponin-1, norepinephrine, procalcitonin, L-lactate, bromate, chlorate, E110, tartrazine, hydrochlorothiazide, human epidermal growth factor-2, lithium,sodium,potassium. This paper provides general summarized information about current aspects of research works related to electrochemical sensors based on molybdenum oxide.

THE EFFECT OF THERMAL ANNEALING AND PULSE LASER ANNEALING IN THE REDUCTION OF GRAPHENE OXIDE

The discovery of Graphene and its unique properties has attracted great interest. Unfortunately, the synthesis of graphene in large scale is challenging, for this reason the derivative of graphene such as graphene oxide (GO) and reduce graphene oxide (rGO) have become alternative sources. The reduction of graphene oxide is an alternative route to obtain graphene-like behavior. This study is aim at examining the similarities and difference between thermal reduction technique and pulse laser method of reduction of (GO). The method utilizes a pulse laser beam for reduction of GO layers on glass substrates and thermal reduction technique. Using the pulse laser method, conductivity of reduced GO was found to be 2.325E-2(1/ohm) which is six times higher than conductivity values reported for GO layers reduced by thermal means at 400oC which was 3.740E-3(1/ohm). A higher transmittance was observed for the pulse laser annealed which holds promising application in a lot technological research. The scanning electron microscope (SEM) result reveals the evenly distribution of the GO around the substrate. The non-thermal nature of the pulse laser method combined with its simplicity and scalability, makes it very attractive for the future manufacturing of large-volume graphene-based optoelectronics

Laser remote monitoring of hazardous substances emissions by ship power plants

При сгорании топлива в судовом двигателе образуются частицы сажи, которые сорбируют в себе токсичные компоненты отработавших газов. Размеры этих частиц варьируются от 0,1 до 100 мкм. В области возможных диапазонов варьирования размеров частиц сажи актуальным является видимая и ближняя ИК-область электромагнитных волн. Решая обратную задачу ослабления и рассеяния света частицами можно получить информацию о концентрации и функции распределения частиц по размерам. Выполнен анализ возможности одновременной оценки концентрации и дисперсности лазерным методом дифференциального ослабления и описан вариант его технической реализации. Разработана четырех волновая лазерная система, которая позволяет измерять сигналы ослабления лазерного излучения методом дифференциального ослабления на трех длинах волн и сигнал рассеяния Ми на частицах аэрозоля излучения четвертого лазера. По измеренным сигналам ослабления рассчитан средний объемно-поверхностный диаметр аэрозольных частиц. Измерены сигналы ослабления лазерного излучения на трех длинах волн на разработанной лазерной установке в составе экспериментального стенда, что позволяет рассчитать значения массовой концентрации и среднего объемно-поверхностного диаметра аэрозольных частиц. Показано, что в зависимости от диапазона размеров частиц сажи выбираются соответствующие длины волн лазерного зондирования. Применение метода дифференциального ослабления лазерного излучения частицами сажи в выбросах судовых энергетических установок на нескольких длинах волн позволяет оценивать одновременно их концентрацию и характеристики дисперсности. When fuel is burned in a marine engine, soot particles are formed that absorb the toxic components of the exhaust gases. The sizes of these particles range from 0.1 to 100 microns. In the range of possible ranges of variation in the size of soot particles, the visible and near-IR regions of electromagnetic waves are relevant. By solving the inverse problem of attenuation and scattering of light by particles, one can obtain information about the concentration and distribution function of particles by size. The analysis of the possibility of simultaneous assessment of the concentration and dispersion by the laser method of differential attenuation is performed and a variant of its technical implementation is described. A four-wave laser system has been developed, which makes it possible to measure the attenuation signals of laser radiation by the differential attenuation method at three wavelengths and the Mie scattering signal on aerosol particles of the radiation of the fourth laser. The measured attenuation signals were used to calculate the average volumetric surface diameter of aerosol particles. The signals of the attenuation of laser radiation at three wavelengths were measured on a developed laser setup as part of an experimental stand, which makes it possible to calculate the values of the mass concentration and the average volume-surface diameter of aerosol particles. It is shown that, depending on the range of size of soot particles, the corresponding laser sounding wavelengths are chosen. The application of the method of differential attenuation of laser radiation by soot particles in the emissions of ship power plants at several wavelengths allows one to evaluate simultaneously their concentration and dispersion characteristics.

OCCURRENCE OF DEFECTS THE PRODUCTION OF MASKS

The article discusses the main stages of the route for the production of masks, during which defects are formed. The main defects and possible reasons for their appearance are given. A method of correcting defects in the form of punctures and undergrowth by the laser method is considered. The disadvantages of the laser method in correcting the elements of the topological pattern of masks are presented.